This proposal is concerned with the aggregation of antibodies on cell surfaces and in solution, and their biological effects. Aggregation of cell surface immunoglobulin (sIg) generates signals that both activate and deactivate B lymphocytes, basophils and mast cells. Our long range goal is to quantitatively understand such signals, and in so doing understand how antigens in allergic reactions activate and desensitize basophils and mast cells. Our approach is to study simple in vitro model systems, to develop mathematical models to describe these systems, and to test these mathematical models against experiment. The role of the mathematical models is to help rigorously test ideas about the system, aid in analyzing experiments, determine parameter values, and suggest new experiments. To study sIg signal generation the project focuses on rat basophilic leukemia (RBL) cells sensitized with hapten-specific monoclonal immunoglobulin E (IgE). Bivalent haptens of different lengths and flexibilities are used to aggregate sIgE. A specific aim is to characterize the binding properties of these bivalent haptens for a few monoclonal IgEs, by using mathematical models to analyze kinetic binding data and obtain rate constants for binding, crosslinking and ring formation. With these constants one can predict how the distribution of sIgE aggregates changes with time. This will be a useful tool in determining what properties of an IgE aggregate make it an effective initiator of a particular response. The RBL cell responses to be studied are degranulation, cytoskeletal interactions, internalization and desensitization. In many in vivo situations, in addition to antigen and specific sIg, solution antibody is present that can bind the antigen. The sera of many allergic individuals contain "blocking" antibody that competes with their specific IgE for antigen. Our goal is to predict under what conditions solution antibody blocks IgE aggregate formation and prevents histamine release and under what conditions it promotes aggregate formation and enhances release. Another type of aggregation process that has quite different biological consequences, occurs in the autoimmune disease systemic lupus erythematosis (SLE) where anti-DNA antibodies bind to DNA in solution. Our aim is to extend the mathematical models of aggregation to anti-DNA/DNA complex formation and develop theories to be used to analyze a variety of antibody/DNA binding experiments.